Answer:
(a) Maximum slope[tex]=\frac {1}{12}[/tex], [tex]H(x)=\frac {1}{12}x[/tex]
(b) 12.5 in.
Step-by-step explanation:
The given condition is the wheelchair ramp must have a maximum rise of 1 in. for every horizontal distance of 12 in.
(a) Let m be the maximum allowable slope for the ramp.
[tex]m=\frac{\text{Maximum rise for the given horozontal disence}}{\text{The given horizontal distance}}[/tex]
[tex]\Rightarrow m=\frac{1}{12}[/tex].
Let x be the distance in the horizontal direction as shown in the figure.
So, for slope m, the linear function H for the height is
[tex]H(x)=mx+C[/tex], where C is constant.
Now, at the starting of the ramp, x=0, and H=0.
Putting this condition back to the equation, we have
[tex]0=m\times 0 +C[/tex]
[tex]\Rightarrow C=0[/tex].
Hence, the required equation is
[tex]H(x)=\frac {1}{12}x[/tex]
(b) The ramp is 150 in. wide,
So, height gained by the ramp at the end is,
[tex]H(x=150)=\frac {1}{12}\times 150=12.5[/tex] in.
